Quantum Chromodynamics (QCD) is currently our best microscopic
description of strong interactions. As is well known, QCD is a gauge
theory with gauge group SU(3), coupling six “flavors” of quarks, which are spin-2 Dirac fermions transforming in
the fundamental representation of the group, to the eight spin-1 gauge
bosons (known as gluons) associated with the local SU(3) symmetry.
Despite their apparently simple form, the interactions of quarks and
gluons, as dictated by the gauge principle and encoded in the Dirac
operator, give rise to a wide variety of phenomena. Most notably, the
low-energy properties of strongly interacting matter are largely
determined by the phenomena of confinement and chiral symmetry
breaking (see, e.g.,
Refs. [1]}, [2]}, [3]}, [4]}). At zero temperature, quarks and gluons are in fact
confined within hadrons by a linearly rising potential, up to
distances where a quark-antiquark pair can be created out of the
vacuum. Furthermore, there is an approximate chiral symmetry
associated with the lightest quarks, which in the limit of exactly
massless quarks is broken spontaneously. This determines most of the
properties of light hadrons, once the effects of the explicit breaking
by the light quark masses is taken into account.
